Officers believe the incident occurred between 9pm and 10.30pm on Saturday, July 12, at The Gym Group in Antelope Park.
The victim had locked their bike at the ground floor facilities before entering the gym and upon returning, they discovered the bike had been stolen, police said.
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In a statement, a spokesperson for Hampshire Constabulary said: “As part of our ongoing enquiries, we are now releasing images of a man we would like to speak to in connection with this incident.
“If you recognise this individual, or have any information that could assist our investigation, please call 101, quoting reference 44250310987.”